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Regresyon Denkleminin Başarısını Ölçmede Kullanılan Belirleme Katsayısı ve Kritiği = Some Critics on the Use of Coefficient of Determination as a Significance Test Criterion for Regression Equation

Author(s): Alptekin GÜNEL

Journal: Dogus University Journal
ISSN 1302-6739

Volume: 4;
Issue: 2;
Start page: 133;
Date: 2003;
Original page

Keywords: Regresyon analizi | Belirleme katsayısı | Regresyon denkleminin testi | Regression analysis | Coefficient of determination | Significance test on regression equation

After introducing briefly the relevant aspects of regression analysis, the article discusses the merit of using the coefficient of determination (R2) as a measure the relative efficiency or predictive precision of a sample linear regression and points out some problems associated with its use. Sample R2 is a biased statistics, however, the bias decreases as the value of R2 increases for the same sample size and for the same number of independent variables. On the other hand, R2 also measures the steepness of the regression equation. If the goodness-of-fit of the regression curve remains constant, R2 increases as the slope of regression surface increases, a fact that appears to be neglected in the relevant literature. Adjusted R2, which is computed by taking the sample size into consideration, assumes negative values when sample size smaller than a threshold value. In short, R2 alone does not reflect the entire picture with respect the efficiency of a sample regression curve; consequently, additional criteria should also be considered in inferring the efficiency of the regression curve, such as sample size, slope of the regression curve, standard error of the equation, ratio of the error variance over R2. Another combination of criteria suggested is adjusted R2 , threshold value of sample size, and the statistics (1 - SY.X /SY).

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